In the making of flexographic printing plates using photo-polymers a mask, typically a halftone film, is placed over a photo-polymer. A traditional halftone film is a film having only two states: fully clear and fully light absorbing (opaque). This is the standard film used in the printing industry for exposing printing plates. In order to print shades of gray, or "gray scale", a technique called screening is used. Each shade of gray is represented by a different size or density of small dots. Thus the film and the plate it produces are binary, having no gray scale. The gray scale is produced by the screening process. The photo-polymer can be a solid or liquid. The photo-polymer is exposed through the film for a few minutes by high power U.V. (ultra violet) light. The clear areas in the mask allow the U.V. light to pass and harden (i.e. cross-link) the photo-polymer. For best results, different areas in the image require different exposures. For example, a single dot on the film surrounded by wide clear areas is sensitive to overexposure, since too much light will cause the dot to disappear due to light leakage into the polymer under the dot (black areas on film become non-printing areas on the plate as the polymer does not harden and is washed away or removed in processing). The opposite is true for a single clear dot in the middle of a large black area of film. The clear dot will not receive sufficient exposure. This problem is well known in the industry and the common solution is to use small pieces of opaque material as masks, to be moved around judiciously during the exposure process. This operation is time consuming and requires a skilled operator to place the small light blocking masks on top of the main mask and remove them at the appropriate point in the exposure. It is the object of the invention to use a variable absorbance mask in order go be able to expose the complete flexographic plate with a single exposure. It is a further object of the invention to produce a flexographic plate with higher resolution than currently possible. In the prior art partial absorbance in mask was used to blend the edges between different masks, as in U.S. Pat. No. 5,286,584, or to reproduce gray scales without screening, as is common in gray scale photographs. The novelty lies in the use of halftones (screening) and gray scales on the same mask.